F# and Monopoly Probabilities

My sons and I were playing Monopoly when we started discussing different strategies for property acquisition. For example, should you try and get Park Place and Boardwalk for the large rent but low probability of someone landing on it or should you get the purples with a high hit chance but lower payout?

We decided to run a simulation and since I an teaching myself F#, we coded up a F# answer. I created a F# Tutorial project and then added a .fsx file. In that file, I first created a couple of variables – 1 of which is a .NET type:

let tiles = [|0 .. 39|]

let random = System.Random()

I then added a Community Chest function that returns a 1 in 16 chance of Going to Jail (board location 10) and a 1 in 16 chance of going to GO (board location 0). This is not completely accurate because we don’t shuffle the deck after every draw – but it seems close enough.

let communityChest x =

let communityChestDraw = random.Next(1,17)

if communityChestDraw = 1 then

0

elseif communityChestDraw = 2 then

10

else

x

I then added a Chance function that did the same thing – with a lot more possibilities (Go to Boardwalk, go to the nearest railroad, etc…)

let chance x =

let chanceDraw = random.Next(1,17)

if chanceDraw = 1 then

0

elseif chanceDraw = 2 then

10

elseif chanceDraw = 3 then

11

elseif chanceDraw = 4 then

39

elseif chanceDraw = 5 then

x – 3

elseif chanceDraw = 6 then

5

elseif chanceDraw = 7 then

24

elseif chanceDraw = 8 then

if x < 5 then

5

elseif x < 15 then

15

elseif x < 25 then

25

elseif x < 35 then

35

else

5

elseif chanceDraw = 9 then

if x < 12 then

12

elseif x < 28 then

28

else

12

else

x

I then added a move function that handled going past the 39th tile and looping around past go and also the “Go to Jail” Tile:

let move x y =

if x + y > 39 then

x + y – 40

elseif x + y = 30 then

10

elseif x + y = 2 then

communityChest 2

elseif x + y = 7 then

chance 7

elseif x + y = 17 then

communityChest 2

elseif x + y = 22 then

chance 22

elseif x + y = 33 then

communityChest 2

elseif x + y = 36 then

chance 36

else

x + y

I then put it together with a simulation function that ran 10000 iterations:

let simulation =

letmutable startingTile = 0

letmutable endingTile = 0

letmutable doublesCount = 0

letmutable inJail = false

letmutable jailRolls = 0

for diceRoll in 1 .. 10000 do

let dieOneValue = random.Next(1,7)

let dieTwoValue = random.Next(1,7)

let numberOfMoves = dieOneValue + dieTwoValue

if dieOneValue = dieTwoValue then

doublesCount <- doublesCount + 1

else

doublesCount <- 0

if inJail = truethen

if doublesCount > 1 then

inJail <- false

jailRolls <- 0

endingTile <- move 10 numberOfMoves

else

if jailRolls = 3 then

inJail <- false

jailRolls <- 0

endingTile <- move 10 numberOfMoves

else

inJail <- true

jailRolls <- jailRolls + 1

else

if doublesCount = 3 then

inJail <- true

endingTile <- 10

else

endingTile <- move startingTile numberOfMoves

let endingTile = move startingTile numberOfMoves

printfn "die1: %A + die2: %A = %A FROM %A TO %A"

dieOneValue dieTwoValue numberOfMoves startingTile endingTile

startingTile <- endingTile

tiles.[endingTile] <- tiles.[endingTile] + 1

I hate the mutable keywords. I don’t know enough about F# to not use it – but it seems that my code is a F# plate of spaghetti

I then spit out the results like this:

let Aggregation =

for tile in tiles do

printfn "%A" tile

And sure enough, I got some results:

I then put these results into Excel where I added the tile names

and did a quick pivot table on property groups like this:

Note that the results seem wrong (or not 100% correct) because Tile #2 (Community Chest) can’t be the most landed on tile and I also had 30 out of the 10,000 times where the cop was the final resting place for a turn – which can’t happen.

If I was using C#, I would have done this in about 25% of the time and been 100% right using unit tests – but I am trying to make myself uncomfortable by learning F# and so I muddle through – often I find that the process is more important than the results in learning.

In any event, I want to make the following changes:

1) Create a tuple using the Tile Name, the PropertyGroup, and the Count

2) Write the unit tests so that I am 100% correct

3) Re-write it getting rid of the mutable keyword

4) Aggregate the list using the F# constrcuts (versus using Excel)

The kids also want to put in the expected rate of return based on the rent for each tile and then the adjustment for each house. That might be fun – but it is irrelevant for actually winning the game (the marginal benefit of additional analysis is very low). As long as you know they key colors and can get monopolies on them (and prevent monopolies by your opponent), you will win more often than not.